Solve the equation by expressing each side as a power of the same base and then equating exponents.
3 (6-3x) = 1/27
{9}
{1/9}
{-3}
{3}
To solve the equation 3(6-3x) = 1/27 by expressing each side as a power of the same base and then equating exponents, we can rewrite the equation using exponentiation.
First, let's rewrite the number 1/27 as a power of the same base as the left side of the equation. The base of the left side is 3, so we need to express 1/27 as a power of 3.
1/27 can be written as 3^(-3) since 3^3 = 27.
Now, we can rewrite the equation as:
3(6-3x) = 3^(-3)
Now, we can equate the exponents:
6 - 3x = -3
Next, let's solve for x in the equation 6 - 3x = -3.
First, let's subtract 6 from both sides of the equation:
6 - 3x - 6 = -3 - 6
-3x = -9
Now, divide both sides of the equation by -3 to solve for x:
-3x / -3 = -9 / -3
x = 3
Therefore, the solution to the equation 3(6-3x) = 1/27 is x = 3.